Question

Dicuss the variation in g with altitude mathematically.....​

Answer 1

Let us consider the earth to be perfectly spherical of mass ‘M’ and radius ‘R’. A body of mass ‘m’ is initially placed on the surface of the earth.

We know,

Acceleration due to gravity is given by

$g1 = \frac{gm}{r {}^{2} }........(1) \\ \\ when \: the \: body \: is \: at \: height \: h. \: \\ g2 \: is \: given \: by \: \: \\ \\ = > g2 = \frac{gm}{(r + h) {}^{2} } .........(2)$

$now \:$

$\frac{g2}{g1} = \frac{r {}^{2} }{(r + h) {}^{2} }$

$= \frac{r {}^{2} }{r {}^{2}(1 + \frac{h}{r}) {}^{2} }$

$= \frac{1}{(1 + \frac{h}{r}) {}^{2} }$

$g2 = g1(1 + \frac{h}{r} ) {}^{ - 2}$

applying binominal expression for

$(1 + \frac{h}{r} ) {}^{ - 2}$

and neglecting higher power of

$\frac{h}{r}$

$= > g2 = g1(1 - \frac{2h}{r} )$

✌✌✌✌✌✌✌✌✌✌✌

thank you ❤❤

Answer 2

Hope it Heplfull Answer

#BadnamBaba